Solve by Factoring 5/(x+8)=3/x

$\frac{5}{x + 8} = \frac{3}{x}$

Step 1

Subtract $\frac{3}{x}$ from both sides of the equation.

$\frac{5}{x + 8} - \frac{3}{x} = 0$

Step 2

Simplify $\frac{5}{x + 8} - \frac{3}{x}$ .

To write $\frac{5}{x + 8}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5}{x + 8} \cdot \frac{x}{x} - \frac{3}{x} = 0$

To write $- \frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 8}{x + 8}$ .

$\frac{5}{x + 8} \cdot \frac{x}{x} - \frac{3}{x} \cdot \frac{x + 8}{x + 8} = 0$

Write each expression with a common denominator of $(x + 8) x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{x + 8}$ by $\frac{x}{x}$ .

$\frac{5 x}{(x + 8) x} - \frac{3}{x} \cdot \frac{x + 8}{x + 8} = 0$

Multiply $\frac{3}{x}$ by $\frac{x + 8}{x + 8}$ .

$\frac{5 x}{(x + 8) x} - \frac{3 (x + 8)}{x (x + 8)} = 0$

Reorder the factors of $(x + 8) x$ .

$\frac{5 x}{x (x + 8)} - \frac{3 (x + 8)}{x (x + 8)} = 0$

Combine the numerators over the common denominator.

$\frac{5 x - 3 (x + 8)}{x (x + 8)} = 0$

Simplify the numerator.

Apply the distributive property.

$\frac{5 x - 3 x - 3 \cdot 8}{x (x + 8)} = 0$

Multiply $- 3$ by $8$ .

$\frac{5 x - 3 x - 24}{x (x + 8)} = 0$

Subtract $3 x$ from $5 x$ .

$\frac{2 x - 24}{x (x + 8)} = 0$

Factor $2$ out of $2 x - 24$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 24}{x (x + 8)} = 0$

Factor $2$ out of $- 24$ .

$\frac{2 x + 2 \cdot - 12}{x (x + 8)} = 0$

Factor $2$ out of $2 x + 2 \cdot - 12$ .

$\frac{2 (x - 12)}{x (x + 8)} = 0$

Step 3

Set the numerator equal to zero.

$2 (x - 12) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (x - 12) = 0$ by $2$ and simplify.

Divide each term in $2 (x - 12) = 0$ by $2$ .

$\frac{2 (x - 12)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x - 12)}{2} = \frac{0}{2}$

Divide $x - 12$ by $1$ .

$x - 12 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x - 12 = 0$

Add $12$ to both sides of the equation.

$x = 12$

Solve by Factoring 5/(x+8)=3/x

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